DETROIT — Jim Schwartz threw a challenge flag when he didn’t need to and the Houston Texans made him regret it.

Shayne Graham’s 32-yard field goal with 2:21 left in overtime lifted Houston to a 34-31 win over the Detroit Lions on Thursday after their coach broke an NFL rule by attempting to challenge a scoring play.

“Obviously that’s a big break in the game for us,” Houston coach Gary Kubiak said. “But I think you make your breaks when you work your tail off.”

Detroit kicker Jason Hanson had a chance to get Schwartz off the hook, but his 47-yard field goal attempt on the fifth possession of the extra period hit the right upright.

Lions defensive end Kyle Vanden Bosch did, too, on the previous possession when he couldn’t intercept a pass Matt Schaub threw directly at him deep in Houston territory.

Detroit might’ve won in regulation if its coach didn’t make a costly mistake.

Schwartz threw a challenge flag when Houston’s Justin Forsett scored on an 81-yard touchdown run in the third quarter after two Lions tackled him.

“Give him credit for continuing to play football,” Kubiak said. “We talk about that all the time. You don’t stop, you play.”

Replays showed Forsett’s left knee and elbow hit the turf near midfield, and the automatic review that accompanies all scoring plays probably would have taken the TD off the board. But NFL rules say that throwing the challenge flag on a scoring play negates the review — and is an unsportsmanlike conduct penalty to boot.

“It’s on me,” Schwartz could be seen saying to assistants and players on the sideline as he tapped his chest. “It’s on me.”

Yes, it was.

Forsett even acknowledged he shouldn’t have allowed to score.

“I know now that I was down, but I didn’t think I was during the play,” he said. “I didn’t think my knee hit, and there was no whistle, so I kept going.

“I wasn’t giving the touchdown back.”

That score pulled Houston within three points.

“I knew the rule — you can’t challenge on a turnover or a scoring play — but I was so mad that I overreacted,” said Schwartz, whose temper got the best of him during a postgame handshake last year with San Francisco coach Jim Harbaugh. “I had the flag in my hand before he even scored because he was obviously down.”

Arian Foster ran for 102 yards and two scores, including a 1-yard run with 1:55 left in the fourth quarter to cap a 15-play, 97-yard drive that tied the game at 31.

AFC South-leading Houston (10-1) took its first lead when Graham made up for missing a field goal earlier in OT after teammate Danieal Manning ripped the football away from Lions tight end Brandon Pettigrew at its 32 on the first drive of the extra period.

The Texans have won five straight — two in a row in OT — and if a handful of teams lose they could be in the playoffs by the time they get back on the practice field after a long weekend.

And, the Lions wilted and blew a fourth-quarter lead during a second straight setback.

Detroit (4-7) has lost three straight to make it extremely difficult to reach its goal of earning a spot in consecutive postseasons for the first time since the mid-1990s.

And as if the Lions don’t have enough problems, defensive tackle Ndamukong Suh could be in trouble with the league again after his left cleat connected with Schaub’s groin area in the first quarter.

“I really don’t have anything to say about that play or that person,” Schaub said.

Suh was on his chest, taken down by an offensive lineman, when he extended his left foot below Schaub’s belt.

It wasn’t clear on replays whether the kick was intentional, but Suh might struggle to get the benefit of doubt and perhaps that’s why he didn’t stick around long enough to talk to reporters after the game.

Last year on Thanksgiving, Suh was ejected for stomping on the right arm of Green Bay offensive lineman Evan Dietrich-Smith and was suspended for two games. He has been fined in previous seasons for roughing up quarterbacks: Cincinnati’s Andy Dalton, Chicago’s Jay Cutler and Cleveland’s Jake Delhomme.

Schaub shook off the blow, stayed in the game, and was 29-of-48 for 315 yards with a 9-yard TD to Owen Daniels to tie the game at 14 late in the first half and an interception.

Houston’s Andre Johnson had nine receptions for 188 yards. Watt had three sacks, one on Detroit’s first snap and the other two that helped the Texans stay within a TD late in the game.

Detroit scored four go-ahead TDs, including on Joique Bell’s 23-yard run early in the fourth quarter, and had a 10-point lead midway through the third quarter.

The Lions drove deep enough into Houston territory in the fourth to put Hanson in a position to give them another 10-point lead, but Watt forced them to punt each time with sacks on third downs.

Stafford was 31-of-61 for 441 yards with two TDs — tiebreaking scores to Calvin Johnson and Mike Thomas in the second quarter — for 441 yards.

Mikel Leshoure ran for 32 yards on 12 carries and gave the Lions their first TD on an opening possession that marked the first rushing score on the ground against Houston.

Those accomplishments along with providing entertainment for the nationally televised audience for a change on Thanksgiving was of little consolation for the franchise.

The Lions lost their previous eight games on the holiday by an averaging of three-plus touchdowns.

Detroit extended the longest losing streak in its annual showcase to nine in a closely contested matchup that will linger in the minds of many people, especially Vanden Bosch, one of many Lions who could’ve changed the outcome by picking off a pass that hit his hands in a wild OT.

“It’s going to be really tough to forget that one,” Vanden Bosch said.

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